Synthesis of a Transfer Function With Real Poles From Tabulated Frequency Response Data for Transmission-Line Impedance Modeling

Synthesis of a transfer function from tabulated frequency response data is an important topic in engineering. Especially in transmission line (TL) modeling, the impedance of a TL must be synthesized in the form of a transfer function of complex frequency, for instance, to be used in time-domain simulations. The TL impedance whose frequency response is in most cases calculated by analytical formulas and prepared in the form of tabulated data shows variation with respect to frequency due to skin effects in conductors and the ground, and synthesis of the frequency variation theoretically requires real poles only. This paper proposes an algorithm to synthesize a transfer function only with real poles from tabulated frequency response data for TL impedance modeling. Since the skin effects are a phenomenon which is continuous with respect to frequency and theoretically does not have poles at specific positions, the problem is essentially to approximate such a frequency response by a transfer function with a finite number of poles. Considering this point, a pole allocation method is investigated using practical TL impedance-matrix data. Once the poles have been allocated, their residue matrices are identified by a least-squares method using the singular value decomposition algorithm with column scaling. For validation, the method is applied to the synthesis of impedance matrices of an overhead power TL and a submarine-cable power TL.